User:Chojullius

Logarithmic Decrement

The logarithmic decrement may be used to estimate the damping ratio of a second order system from an oscillatory response. The logarithmic decrement is defined as the natural log of the ratio of the size of two peaks, n periods apart:${\displaystyle \delta _{n}=ln({\frac {P_{i}}{P_{i+n}}})}$. This ratio may be used to estimate the damping ratio with following equation:${\displaystyle \varsigma ={\frac {\delta _{n}}{((n+2{\pi })^{2}+{(\delta _{n})^{2}})^{1/2}}}}$